1. Field of the Invention
The present invention relates generally to the determination of the rotary position and velocity of a rotating apparatus, and more specifically to the accurate determination of the position of a xerographic photoreceptor belt being driven by a rotating drive roller having a low resolution encoder attached thereto.
2. Description of the Prior Art
In the measurement of position and velocity of rotating elements, such as drive rollers for a xerographic photoreceptor belt, it is common practice to utilize encoders to monitor the position of the rotating element. In general, however, the accuracy of the positional information is limited to the resolution of the encoder used. It is also generally known that in order to increase the accuracy of the positional information more expensive, high resolution encoders must be employed. Moreover, the same high resolution encoders are required to accurately determine the velocity of a rotating element.
Other methods of characterizing the motion of a rotating element are disclosed in the following references. For example, U.S. Pat. No. 4,716,535 to Yoshida et al. discloses a speed detection apparatus for detecting the speed of a rotary machine, or any mechanism which generates pulses at a frequency proportional to its speed. The speed detection apparatus comprises a pulse generator for generating signal pulses proportional to the speed of the machine; a sampling interval setting unit; a counting unit for counting signal pulses generated by the pulse generator in accordance with a sampling interval; and a calculating unit for determining the speed of the machine.
U.S. Pat. No. 4,639,884 to Sagues discloses a combination of hardware and microprocessor driven software for measuring the rotary velocity of a servo shaft driven by a motor. A square wave signal is produced according to the rotation of the shaft, while a high speed clock produces a large number of clock pulses in order to count transitions of the square wave. The total number of transitions of the square wave during a selected time period is divided by the total number of clock pulses during the same period in order to determine the velocity of the shaft.
U.S. Pat. No. 4,162,443 to Brearly et al. discloses a method and apparatus for measuring the frequency of a pulse signal generated by a transducer which may be used to sense engine speed. The frequency of the pulse signal is measured by counting the number of complete pulse cycles and measuring the fractional value of any incomplete pulse cycle occurring during a fixed sampling period. The number of complete pulse cycles and the fractional value of any incomplete pulse cycle are summed to obtain a total number of pulses during the sampling period. The fractional value of pulse cycles during the sampling period is determined using a clock pulse signal having a base frequency, where the total number of clock pulse signals occurring during a complete cycle increase in proportion to the number of complete cycles within a sampling period. A computer divides the number of clock pulses occurring during the fractional cycle by the frequency corrected number of clock pulses occurring during the previous complete cycle to determine the fractional value and enabling calculation of the speed.
U.S. Pat. No. 4,224,568 to Griner discloses a method for measuring the number of full and fractional cycles of a periodically time varying signal during a fixed sampling period. The end fractional cycle occurring during a sampling period is measured by (1) counting the number of clock pulses occurring during the last full cycle of the sampling period; and (2) counting the the number of clock pulses occurring between the end of the last full cycle in the sample period and the end of the sample period. The number of clock pulses counted in (1) is divided by the number of clock pulses counted in (2) to determine the end fractional cycle. The end fractional cycle is also used, by subtracting it from unity, to estimate a front fractional cycle which will be summed in the subsequent sampling period to determine the total number of cycles occurring in the sampling period.
U.S. Pat. No. 4,251,869 to Shaffer discloses a frequency-to-binary converter, operable in conjunction with a digital computer, which measures a square wave signal to determine its frequency during a fixed time interval. The number of completed wave periods within the time interval are measured, and the number of fractional wave periods are also calculated. Given the whole and fractional periods, the computer calculates the wave frequency according to a programmed equation.
In general, the references cited above disclose systems suitable for determination of the instantaneous velocity or frequency of a system having a characteristic output signal that varies periodically with time. Generally, these system are suitable for providing feedback to a velocity control system that would then alter the drive motor velocity until the measured velocity was within an acceptable range of the target drive motor velocity. The references cited above disclose systems which provide instantaneous velocity feedback. Unfortunately, such a system does not provide feedback information relating to the positional change of the rotating element being monitored, other than the positional change that occurred over the most recent sampling interval. As an example, if the rotating body were temporarily halted, a velocity-only feedback system, as cited in the references, would detect a decrease in velocity and signal only the detected decrease in velocity. Having velocity-only feedback, the control system would respond by signaling the drive motor to increase velocity until the appropriate velocity was once again reached. However, such a system would not have any indication of the relative position differential caused by the momentary stoppage of rotation and, therefore, could not be used to control the motor in an effort to regain the lost distance.
In a xerographic system, it is necessary to monitor and control not only the velocity of the photoreceptor belt, but also the relative position of the belt, via the associated drive roll, to assure that the belt is advancing in the required manner. A velocity-only feedback system would provide no indication of the position of the belt and would, therefore, be unacceptable. Fortunately, a position-velocity feedback system would provide the necessary information to control the velocity and position of the photoreceptor belt.
It is therefore an object of the present invention to provide a system capable of determining the position of a rotating body, or element driven therefrom, in a highly accurate manner and to utilize the positional information to determine the velocity of the rotating body. It is a further object of the present invention to utilize a low or moderate resolution encoder attached to such a body to enable the high accuracy determination of the body's position. It is another object of the present invention to reduce the positional error built up within a sampling type monitoring system by cumulatively tracking the position of the rotating body over all sampling intervals. It is a final object of the present invention to utilize such a positional tracking system to monitor the position and velocity of a belt driven photoreceptor in order to accurately monitor and control the xerographic processes operatively associated with latent images formed thereon.
Further advantages of the present invention will become apparent as the following description proceeds and the features characterizing the invention will be pointed out with particularity in the claims annexed to and forming a part of this specification.